Smallest Missing Integer Greater Than Sequential Prefix Sum

Smallest Missing Integer Greater Than Sequential Prefix Sum

What is this problem about?

The "Smallest Missing Integer Greater Than Sequential Prefix Sum" interview question asks you to find a specific missing value based on an array's longest sequential prefix. First, you find the longest prefix that is a sequential sequence (e.g., 1, 2, 3). You sum these values. Then, you find the smallest integer that is greater than or equal to this sum and is not present anywhere in the original array. This "Smallest Missing Integer Greater Than Sequential Prefix Sum coding problem" combines prefix logic with set-based lookups.

Why is this asked in interviews?

Companies like Microsoft and Meta ask this to test basic array processing and the use of hash sets for efficient lookup. It's an "EASY" problem that evaluates if a candidate can handle multi-step instructions without getting confused. It also checks for "edge case" thinking—what if the sequential prefix is just the first element?

Algorithmic pattern used

This follows the "Array and Hash Table interview pattern".

1. Identify the longest sequential prefix: Start from the first element and keep adding to the sum as long as nums[i] == nums[i-1] + 1.
2. Store all elements of the array in a Hash Set for O(1) lookups.
3. Start a variable ans at the calculated prefix sum.
4. While ans is in the Hash Set, increment ans.
5. Return ans.

Example explanation

Array: [3, 4, 5, 1, 10]

1. Sequential Prefix: 3, 4, 5. (6 is not 1, so it stops).
2. Prefix Sum: 3 + 4 + 5 = 12.
3. Array Set: {1, 3, 4, 5, 10}.
4. Is 12 in Set? No. Result: 12. If the array was [1, 2, 3, 2, 5], sum is 6. If 6 was in the array, we would check 7, and so on.

Common mistakes candidates make

A common error is looking for the sequential sequence anywhere in the array instead of strictly as a prefix starting at index 0. Another mistake is forgetting to include the original array elements in a set, making the search for the "missing" integer O(N^2) instead of O(N). Some candidates also misinterpret "greater than or equal to," starting their search at sum + 1 instead of sum.

Interview preparation tip

When you need to check if multiple values exist in an array, always convert the array to a Set first. This reduces your search time from linear to constant, which is a fundamental optimization in any "Smallest Missing Integer Greater Than Sequential Prefix Sum interview question".